I am looking at swap curve building at front end and find it difficult to get a smooth forward curve with a fast generic algorithm. For example, EUR 6m curve has 6m deposit, and then a series of FRAs (1m by 7m, 2m by 8m,,,,etc) up to 2 year swap at front end. If I use a naive smooth interpolation method such as cubic spline and use 6m, 7m, 8m,..., as knot points on the spline, I get very unsmooth/jumpy forward curve. I also tried monotone-convex method in Hagan's paper, it gets much smoother, however, on a few days, the curve still gets very jumpy. One way to address is to add "synthetic" deposit before 6m. However, I want to apply a more generic algorithm to fit to this type of structure. I am thinking I can use some shape preserving algorithm: minimize the length of the forward curve with all the market instruments being repriced. However, with a polynomial spline, this optimization method will take some time to solve. Can I assume a piece-wise linear but continuous forward rate and set up this optimization problem just for the front end? (since they are densely spaced, I wonder if a high order polynomial is needed anyway). Did anyone try this approach before? Also does anyone know what is the approach taken at banks nowadays to address issue like this? Or is there any paper on this topic? Thank you.


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